Trigonometry in the minkowski plane

Francesco Catoni, Dino Boccaletti, Roberto Cannata, Vincenzo Catoni, Enrico Nichelatti, Paolo Zampetti

Research output: Contribution to journalArticle

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Abstract

We have seen in Section 3.2 how commutative hypercomplex numbers can be associated with a geometry, in particular the two-dimensional numbers can represent the Euclidean plane geometry and the space-time (Minkowski) plane geometry. In this chapter, by means of algebraic properties of hyperbolic numbers, we formalize the space-time geometry and trigonometry. This formalization allows us to work in Minkowski space-time as we usually do in the Euclidean plane, i.e., to give a Euclidean description that can be considered similar to Euclidean representations of non-Euclidean geometries obtained in the XIXth century by E. Beltrami on constant curvature surfaces, as we recall in Chapter 9. © 2008 Birkhäuser Verlag AG.
Original languageEnglish
Pages (from-to)27 - 56
Number of pages30
JournalFrontiers in Mathematics
Volume2008
DOIs
Publication statusPublished - 2008
Externally publishedYes

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All Science Journal Classification (ASJC) codes

  • Mathematics (miscellaneous)

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